Mathematics of FinanceMCQMTP Sep 24 Series IQuestion 1425 of 512
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If the interest rate on a loan at 1%\displaystyle 1\% per month, the effective annual rate of interest is:

Options

A12%\displaystyle 12\%
B12.36%\displaystyle 12.36\%
C12.68%\displaystyle 12.68\%
D12.84%\displaystyle 12.84\%
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Correct Answer

Option c12.68%\displaystyle 12.68\%

All Options:

  • A12%\displaystyle 12\%
  • B12.36%\displaystyle 12.36\%
  • C12.68%\displaystyle 12.68\%
  • D12.84%\displaystyle 12.84\%

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Detailed Solution & Explanation

Given parameters: * Monthly Interest Rate (i\displaystyle i) = 1%\displaystyle 1\% per month =0.01\displaystyle = 0.01 * Number of compounding periods per year (m\displaystyle m) = 12\displaystyle 12 The formula for the effective annual rate of interest (E\displaystyle E) is: E=(1+i)m1E = (1 + i)^m - 1 Substituting the values: E=(1+0.01)121E = (1 + 0.01)^{12} - 1 E=(1.01)121E = (1.01)^{12} - 1 First, let's calculate (1.01)12\displaystyle (1.01)^{12}: (1.01)121.126825(1.01)^{12} \approx 1.126825 Thus: E1.1268251=0.126825=12.68%E \approx 1.126825 - 1 = 0.126825 = 12.68\% The effective annual rate of interest is 12.68%\displaystyle 12.68\%. Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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